Fuzzy Set Theory and Advanced Mathematical Applications contains contributions by many of the leading experts in the field, including coverage of the mathematical foundations of the theory, decision making and systems science, and recent developments in fuzzy neural control. The book supplies a readable, practical toolkit with a clear introduction to fuzzy set theory and its evolution in mathematics and new results on foundations of fuzzy set theory, decision making and systems science, and fuzzy control and neural systems. Each chapter is self-contained, providing up-to-date coverage of its subject. Audience: An important reference work for university students, and researchers and engineers working in both industrial and academic settings.

Decision modeling is a key area in the developing field of AI, and this timely work connects researchers and professionals with the very latest research. It constitutes the refereed proceedings of the 4th International Conference on Modeling Decisions for Artificial Intelligence, held in Kitakyushu, Japan, in August 2007. The 42 revised full papers presented together with 4 invited lectures are devoted to theory and tools, as well as applications.

Topics in this book range from mathematical theories to probabilistic analysis of structures in civil engineering. Mathematical background is first covered including: probabilistic and possibilistic conceptualization of uncertainty, the algebraic structure of conditional reasoning, uncertainty modeling in anticipatory systems, reasoning by hypothesizing causal models, fuzzy sets and truth functionality. The second part deals with expert systems and neuronal structures and includes papers on expert appraisement and counter-appraisement with experton processes, the management of uncertainty, transferable belief models for expert judgement, fuzzy neural expert systems, and inverse dynamic adaptive control. Of particular interest is the last section which deals with applications in engineering. The articles presented here show just how far this field has progressed from theory to practice. They deal with such topics as the prediction of earthquake ground motion and structural responses, bridge ratings, safety and reliability evaluations of transmission lines, and transportation.

The non-Newtonian calculi provide a wide variety of mathematical tools for use in science, engineering, and mathematics. They appear to have considerable potential for use as alternatives to the classical calculus of Newton and Leibniz. It may well be that these calculi can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.

Due to inherent limitations in human sensing organs, most data collected for various purposes contain uncertainties. Even at the rare occasions when accurate data are available, the truthful predictions derived on the data tend to create chaotic consequences. So, to effectively process and make sense out of available data, we need methods to deal with uncertainty inherently existing inside the data. The intent of this monograph is to explore the fundamental theory, methods, and techniques of practical application of grey systems theory, initiated by Professor Deng Julong in 1982. This volume presents most of the recent advances of the theory accomplished by scholars from around the world. From studying this book, the reader will not only acquire an overall knowledge of this new theory but also be able to follow the most current research activities. All examples presented are based on practical applications of the theory when urgent real-life problems had to be addressed. Last but not the least, this book concludes with three appendices. The first one compares grey systems theory and interval analysis while revealing the fact that interval analysis is a part of grey mathematics. The second appendix presents an array of different approaches of studying uncertainties. And, the last appendix shows how uncertainties appear using general systems approach.

2.1 Text Summarization “Text summarization is the process of distilling the most important information from a source (or sources) to produce an abridged version for a particular user (or users) and task (or tasks)” [3]. Basic and classical articles in text summarization appear in “Advances in automatic text summarization” [3]. A literature survey on information extraction and text summarization is given by Zechner [7]. In general, the process of automatic text summarization is divided into three stages: (1) analysis of the given text, (2) summarization of the text, (3) presentation of the summary in a suitable output form. Titles, abstracts and keywords are the most common summaries in Academic papers. Usually, the title, the abstract and the keywords are the first, second, and third parts of an Academic paper, respectively. The title usually describes the main issue discussed in the study and the abstract presents the reader a short description of the background, the study and its results. A keyword is either a single word (unigram), e.g.: ‘learning', or a collocation, which means a group of two or more words, representing an important concept, e.g.: ‘machine learning', ‘natural language processing'. Retrieving collocations from text was examined by Smadja [5] and automatic extraction of collocations was examined by Kita et al. [1].